Journal of Symbolic Logic

Hybrid Logics: Characterization, Interpolation and Complexity

Carlos Areces, Patrick Blackburn, and Maarten Marx

Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR.

Abstract

Hybrid languages are expansions of propositional modal languages which can refer to (or even quantify over) worlds. The use of strong hybrid languages dates back to at least [Pri67], but recent work (for example [BS98, BT98a, BT99]) has focussed on a more constrained system called $\mathscr{H}(\downarrow, @)$. We show in detail that $\mathscr{H}(\downarrow, @)$ is modally natural. We begin by studying its expressivity, and provide model theoretic characterizations (via a restricted notion of Ehrenfeucht-Fraisse game, and an enriched notion of bisimulation) and a syntactic characterization (in terms of bounded formulas). The key result to emerge is that $\mathscr{H}(\downarrow, @)$ corresponds to the fragment of first-order logic which is invariant for generated submodels. We then show that $\mathscr{H}(\downarrow, @)$ enjoys (strong) interpolation, provide counterexamples for its finite variable fragments, and show that weak interpolation holds for the sublanguage $\mathscr{H}$(@). Finally, we provide complexity results for $\mathscr{H}$(@) and other fragments and variants, and sharpen known undecidability results for $\mathscr{H}(\downarrow, @)$.

Article information

Source
J. Symbolic Logic, Volume 66, Issue 3 (2001), 977-1010.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183746543

Mathematical Reviews number (MathSciNet)
MR1856725

Zentralblatt MATH identifier
0984.03018

JSTOR
links.jstor.org

Citation

Areces, Carlos; Blackburn, Patrick; Marx, Maarten. Hybrid Logics: Characterization, Interpolation and Complexity. J. Symbolic Logic 66 (2001), no. 3, 977--1010. https://projecteuclid.org/euclid.jsl/1183746543


Export citation